Chapter 5, Problem 2PA

Support activity cost allocation

Jake’s Gems mines and produces diamonds, rubies, and other gems. The gems are produced by way of the Mining and Cutting activities. These production activities are supported by the Maintenance and Security activities. Security costs are allocated to the production activities based on asset value. Maintenance costs are normally allocated based on machine hours. However, Maintenance costs typically correlate more with the number of service calls. Information regarding the activities is provided in the following table:

Instructions

1. Should Maintenance costs continue to be allocated based on machine hours? Why would a different driver be more appropriate?

2. Based on your response to part (1), determine the total costs allocated from each support activity to the other activities using the reciprocal services method and the most appropriate cost driver for Maintenance.

3. Jake’s Gems is considering cutting costs by switching to a simpler support activity cost allocation method. Using the information provided and given your response to part (2), determine if switching to the direct method would significantly alter the production activity costs.

To determine

Identify the cost driver to allocate maintenance costs and whether or not to use the machine hours as the cost driver.

Explanation of Solution

Cost Driver: The cost driver refers to the all the activities on which the money is spent to produce the product or the service. It has a cause-effect relationship with the resources utilized in production. The cost drivers are used to form the activity cost pools.

The support department costs in the production are the indirect costs that difficult to identify and be associated to the concerned cost drivers. Hence, it is difficult to apply support department costs to the products.

Machine hours are not an accurate cost driver and must not be used. Service calls must be used as it a more appropriate cost driver as maintenance department is associated more with the service calls rather than the machine hours.

To determine

Compute the total cost of each production department after allocating all support costs to the production departments using the cost driver chosen in part a.

Explanation of Solution

Maintenance Department Cost to be allocated:

The total Maintenance Department costs include 25% of the Security department costs as,

$\frac{200,000}{\left(200,000+300,000+300,000\right)}$.

Therefore, the Security Department cost is,

$\text{Maintenance department = \$25,000 + }\left(\text{0}\text{.25}\times \text{S}\right)$

Security Department Cost to be allocated:

The total Security Department costs include 20% of the Maintenance department costs as,

$\frac{20}{\left(20+60+20\right)}$.

Therefore, the Security Department cost is,

$\text{Security department = \$42,500 + }\left(\text{0}\text{.2}\times \text{M}\right)$

Substitute the equation for M into the S equation:

$\begin{array}{c}\text{Security department = \$42,500 + }\left[\text{0}\text{.2}\times \left[\text{\$25,000 + }\left(\text{0}\text{.25}\times \text{S}\right)\right]\right]\\ =\text{\$42,500 +\$5,000 + }\left(\text{0}\text{.05}\times \text{S}\right)\\ 0.95\times \text{S}=\text{\$47,500}\\ \text{= \$50,000}\end{array}$

Substitute the value of S into the M equation:

$\begin{array}{c}\text{Maintenance department = \$25,000 + }\left(\text{0}\text{.25}\times \text{\$50,000}\right)\\ =\text{\$25,000 +\$12,500 }\\ \text{= \$37,500}\end{array}$

Maintenance Department Cost Allocation:

Compute the allocation of costs from Maintenance Department to Security Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Security Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{20}{\left(20+60+20\right)}\times 100\right)\times \$37,500\\ =20\%\times \$37,500\\ =\$7,500\end{array}$

The cost allocated from Maintenance Department to Security Department is $7,500.

Compute the allocation of costs from Maintenance Department to Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{20}{\left(20+60+20\right)}\times 100\right)\times \$37,500\\ =20\%\times \$37,500\\ =\$7,500\end{array}$

The cost allocated from Maintenance Department to Cutting Department is $7,500.

Compute the allocation of costs from Maintenance Department to Mining Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Mining Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{60}{\left(20+60+20\right)}\times 100\right)\times \$37,500\\ =60\%\times \$37,500\\ =\$22,500\end{array}$

The cost allocated from Maintenance Department to Mining Department is $22,500.

Security Department Cost Allocation:

Compute the allocation of costs from Security Department to Maintenance Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Maintenance Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{200,000}{\left(200,000+120,000+480,000\right)}\times 100\right)\times \$50,000\\ =25\%\times \$50,000\\ =\$12,500\end{array}$

The cost allocated from Security Department to Maintenance Department is $12,500.

Compute the allocation of costs from Security Department to Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{480,000}{\left(200,000+120,000+480,000\right)}\times 100\right)\times \$50,000\\ =60\%\times \$50,000\\ =\$30,000\end{array}$

The cost allocated from Security Department to Cutting Department is $30,000.

Compute the allocation of costs from Security Department to Mining Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Mining Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{120,000}{\left(200,000+120,000+480,000\right)}\times 100\right)\times \$50,000\\ =15\%\times \$50,000\\ =\$7,500\end{array}$

The cost allocated from Security Department to Mining Department is $7,500.

Total Costs of Production Departments:

Compute the total cost of the Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Cutting}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Maintenance }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the }\\ \text{Security}\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Cutting}\\ \text{Department}\end{array}\right)\\ \text{= \$7,500 + \$30,000 + \$95,000}\\ \text{= \$132,500}\end{array}$

The total costs of the Cutting department are $132,500.

Compute the total cost of the Mining Department:

$\begin{array}{c}\begin{array}{l}\text{Mining}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Maintenance }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the }\\ \text{Security}\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Mining}\\ \text{Department}\end{array}\right)\\ \text{= \$22,500 + \$7,500 + \$160,000}\\ \text{= \$190,000}\end{array}$

The total costs of the Pruning department are $190,000.

To determine

Identify the impact on the costs if company switches to simpler cost allocation method than the one used in part (b).

Explanation of Solution

Maintenance Department Cost Allocation:

Compute the allocation of costs from Maintenance Department to Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{20}{60+20}\times 100\right)\times \$25,000\\ =25\%\times \$25,000\\ =\$6,250\end{array}$

The cost from Maintenance Department that should be allocated to Cutting department is $6,250.

Compute the allocation of costs from Maintenance Department to Mining Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Mining Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{60}{60+20}\times 100\right)\times \$25,000\\ =75\%\times \$25,000\\ =\$18,750\end{array}$

The cost allocated from Maintenance Department to Pruning department is $18,750.

Security Department Cost Allocation:

Compute the allocation of costs from Security Department to Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{480,000}{\left(120,000+480,000\right)}\times 100\right)\times \$42,500\\ =80\%\times \$42,500\\ =\$34,000\end{array}$

The cost allocated from Security Department to Cutting department is $34,000.

Compute the allocation of costs from Security Department to Pruning Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Mining Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{120,000}{\left(120,000+480,000\right)}\times 100\right)\times \$42,500\\ =20\%\times \$42,500\\ =\$8,500\end{array}$

The cost allocated from Security Department to Pruning department is $8,500.

Total Costs of Production Departments:

Compute the total cost of the Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Cutting}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Maintenance }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the }\\ \text{Security }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Cutting}\\ \text{Department}\end{array}\right)\\ \text{= \$6,250 + \$34,000 + \$95,000}\\ \text{= \$135,250}\end{array}$

The total costs of the Cutting department are $135,250.

Compute the total cost of the Mining Department:

$\begin{array}{c}\begin{array}{l}\text{Mining}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Maintenance }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the }\\ \text{Security}\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Mining}\\ \text{Department}\end{array}\right)\\ \text{= \$18,750 + \$8,500 + \$160,000}\\ \text{= \$187,250}\end{array}$

The total costs of the Pruning department are $187,250.

The switch from the existing method to the direct method would ensure the reduction of cost also there is a very little change in the costs being allocated amongst the two methods.